Let C be the cube with set of vertices {(x,y,z) $\in R^3$  : x,y,z  $\in$  {-1,1}}. Let  $D_f$  be the set of all twelve lines containing the diagonals of the six faces of the cube C. Let  $D_m$  be the set of all four lines containing the main diagonals of the cube C ; for instance, the line passing through the vertices

( -1, -1,-1) and (1,1,1) is in  $D_m$. Let  d  $({\mathcal{l}}_1,{\mathcal{l}}_2)$ denotes the shortest distance between lines  ${\mathcal{l}}_1$  and  ${\mathcal{l}}_2$. If  the maximum value of  d $({\mathcal{l}}_1,{\mathcal{l}}_2)$, as  ${\mathcal{l}}_1$ varies over $D_f$  and  ${\mathcal{l}}_2$  varies over   $D_m$ is equal to  $\lambda$ , then  ${\lambda }^{-2}$ equals